Tucked down a side street a few minutes' swagger from a drab, graffiti-covered bus station, the "Eastwear" clothes store in Zwickau has everything today's smartly dressed neo-Nazi-about-town could want.

As well as shirts and bomber jackets by the leisure brand Thor Steinar – Germany's answer to the British skinhead favourites Fred Perry and Lonsdale – there is an extensive wardrobe for those who like their tailoring with rather more attitude, from "Hooligan" brand gloves through to "Hatewear" and "Iron Fist" sweatshirts.

Last week, though, the most sinister item on show was not the T-shirt with the knuckle-duster and crossed baseball bat motif, but the T-shirt pinned to the front counter with a cartoon of the Pink Panther, bearing the logo "Staatsfeind", or "enemy of the state".

"It's just a logo, it doesn't have anything to do with neo-Nazi politics," insisted the shop assistant, who identified himself only as Thomas, when asked why he had it pinned to the front of his counter. "Eighty per cent of our customers are just normal people anyway, and besides, real neo-Nazis wouldn't buy clothes here – they'd want to stay undetected."

So why, then, did he anxiously whisk the T-shirt from the display and hide it behind the counter? An obvious clue can be found by visiting a quiet suburban street on the far side of Zwickau, where two weeks ago, a grisly chain of events proved that "real" neo-Nazis do indeed go for more than just fashion statements.

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There, at 26 Fruhlingsstrasse, a police cordon still surrounds the charred remains of a yellow, three-storey wooden house that is the last known address of Uwe Mundlos, 38, his friend Uwe Böhnhardt, 34, and their alleged female accomplice Beate Zschäpe, 36, all said to be core members of the self-styled National Socialist Underground.

A secret cell dedicated to creating a Fourth Reich, its members are thought to have gunned down eight Turks, a Greek, and a German policewoman since 1998, as well carrying out 14 bank robberies and two bombings.

Yet their 13-year crime spree came to light only on the afternoon of November 4, when the bodies of Mundlos and Böhnhardt were found in a camper van in a nearby town, having apparently killed themselves after robbing a building society that morning.

Just hours afterwards, their flat in Zwickau was set ablaze allegedly by Miss Zschäpe, who turned herself into police, reportedly saying: "I'm the one you're looking for."

By then, though, detectives already had no shortage of evidence to go on. Found in the wreckage of the fire was the Czech-made pistol used in the killings of the nine foreigners, and also one belonging to the murdered policewoman. And as if to remove any doubts, police also discovered a home-made DVD, in which a computer mock-up of the Pink Panther cartoon embarked on a "tour" of the different murder scenes. Chillingly, it included footage that only someone present at the killings could have shot.

Germans have been shocked by the existence of the group, likened to a far-Right version of the Baader-Meinhof gang, which waged a similar campaign of urban terror on behalf of the far-Left in the 1970s.

But as well as awakening the much older spectre of the country's Nazi past, what has proved far more embarrassing is that they went entirely undetected by the German authorities. Instead, the police were convinced that the murders were the work of Greek and Turkish mafiosi, an assumption that has now brought them unflattering comparisons to Inspector Clouseau, the Pink Panther's inept detective.

"The police kept looking for dodgy business dealings supposedly done by my father," said Gamze Kubasik, 22, the daughter of Mehmet Kubasik, 39, who was shot dead at his newspaper kiosk in 2006. "They didn't take seriously our suspicion that it could have been neo-Nazis."

Quite why the group chose the Pink Panther to adorn their Blair Witch-style video epitaph remains unclear. Unlike deathsheads, swastikas and pagan rune symbols, it seems to have no wider currency among the far-Right movement, although it was also found on the Facebook page of Peter Klose, a former leader in Zwickau of the far-right National Democratic Party (NPD).

Last week he claimed the Pink Panther logo was "purely coincidental" – remarkable, indeed, given that it is also on display in Thomas's shop.

If the German authorities know the significance of the logo, they are not saying yet. But it is clear that they have much more information on the gang. The trio first came to their attention in the mid 1990s, when they belonged to a far-Right Kameradschaft, or comradeship group, in the east German town of Jena, where they all grew up.

Germany's equivalent of MI5 had 24 fat files on the group's activities, including details of Böhnhardt's arrest for hanging a Jewish mannequin from a highway bridge, and Miss Zschäpe being charged with hate speech for having a Monopoly board with a "concentration camp" instead of a "jail" square.

But in 1998, after being accused of a pipe bomb plot, the three went on the run – remaining free despite what German police claimed was an "extensive manhunt".

Some believe that Germany's recent experience of Islamic terrorists – in particular the so-called Hamburg cell, who were key to the September 11 attacks – led the country's security services to overlook domestic threats.

Chancellor Angela Merkel, who held a meeting about the killings on Friday, has called for a review of whether the NPD should be banned altogether, while the interior minister, Hans-Peter Friedrich, now wants a national register of "all potentially violent Right-wing extremists".

Both proposals have prompted pledges of a court challenge by Frank Scherdt, the NPD deputy leader, whose movement sees itself as no different to the British National Party, with which it has close ties.

"We were as shocked by these killings as anyone," said Mr Scherdt, 67, in an interview at his party's offices in east Berlin, which is heavily fortified to fend off attack by "anti-fascist" groups. "These people have nothing to do with us, and this incident is simply being used to discredit us."

Mr Friedrich also wants an inquiry into the far-Right scene in places such as Zwickau, one of dozens of depressed towns in the former East Germany where neo-Nazism has thrived since the Berlin Wall came down. Once famous as the town that made the Communist regime's Trabant cars, Zwickau now seems little different to the West except for the odd derelict Soviet-era building and the presence of Russian borsch soup on restaurant menus.

But unemployment remains high, leaving plenty of bored youths for "comradeship" groups to recruit, according to Rene Hahn, 30, a councillor with the Left Party. "Support for neo-Nazism is fairly static, but comradeship groups do attract people with activities like going to football matches and music concerts," he said.

Mr Hahn tries to combat this by running youth workshops of his own, giving talks on democracy and pointing youngsters in the direction of anti-fascist punk bands rather than the skinhead ones.

Yet if the background of people like Mundlos is anything to go by, well-intended "anti-fascist action" programmes could be the problem rather than the solution. Like many other east German neo-Nazis, Mundlos had spent his youth being force-fed such propaganda by the Communist authorities.

Embracing the far-Right, it seems, may have been as much an act of youthful rebellion for a former East German as embracing the far-Left was for the Baader-Meinhof.

"The fall of the Wall left a huge vacuum, with no good role models for young people," said Lothar Koenig, a priest and youth worker from Jena. "Everything they'd been told to believe in was destroyed overnight."

As, too, has Germany's hope that its Nazi era might soon be something that no longer comes back to haunt it. The Turkish government has demanded an explanation of why the killers went undetected for so long, claiming that the three million Turkish workers in Germany deserve better protection.

Meanwhile, the German police, who have already discovered that the group had a hit list of 88 additional targets, including MPs and immigrant leaders, are urgently investigating whether the residents of 26 Fruhlingsstrasse might be part of a much wider network. With the body count so high already, nobody wants to find a DVD marked "Return of the Pink Panther".